On the quantum-mechanics of a single photon

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Abstract

It is shown that a Dirac(-type) equation for a rank-two bi-spinor field ψph on Minkowski (configuration) spacetime furnishes a Lorentz-covariant quantum-mechanical wave equation in position-space representation for a single free photon. This equation does not encounter any of the roadblocks that have obstructed previous attempts (by various authors) to formulate a quantum-mechanical photon wave equation. In particular, it implies that the photon wave function ψph yields conserved non-negative Born-rule-type quantum probabilities and that its probability current density four-vector transforms properly under Lorentz transformations. Moreover, the eigenvalues of the pertinent photon Dirac Hamiltonian and the vector eigenvalues of the photon momentum operator yield the familiar Einstein relations E = ω and p = k, respectively. Furthermore, these spin-1 wave modes are automatically transversal without the need of an additional constraint on the initial data. Some comments on other proposals to set up a photon wave equation are supplied as well.

Original languageEnglish (US)
Article number112302
JournalJournal of Mathematical Physics
Volume59
Issue number11
DOIs
StatePublished - Nov 1 2018

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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